Henry had 40% more erasers than Harper. Hazel had 20% fewer erasers than Henry. Henry and Harper gave Hazel some erasers in the ratio of 3 : 4. As a result, Hazel had 50% more erasers than before. Given that Hazel had 175 more erasers than Harper in the end, how many erasers did Henry give to Hazel?

Henry	Harper	Hazel
7x5	5x5
5x7		4x7
35	25	28

100% + 40% = 140%
140% = ¹⁴⁰₁₀₀ = ⁷₅

Henry : Harper = 7 : 5

100% - 20% = 80%
80% = ⁸⁰₁₀₀ = ⁴₅

Henry : Hazel = 5 : 4

The number of erasers that Henry had at first is repeated. Make the number of erasers that Henry had at first the same.  LCM of 7 and 5 is 35.

	Henry	Harper	Hazel
Before	35x1 =  35 u	25x1 = 25 u	28x1 = 28 u
Change			+ 14x1 = + 14 u
Comparing the changes in the number of erasers	- 3x2 = - 6 u	- 4x2 = - 8 u	+ 7x2 = + 14 u
After	29 u	17 u	42x1 = 42 u

50% x 28 
= ⁵⁰₁₀₀ x 28 
= 14 

The total number of erasers that Henry and Harper gave to Hazel is repeated.  Make the total number of erasers that Henry and Harper gave to Hazel the same.  LCM of 7 and 14 is 14.

Number of erasers that Hazel had more than Harper 
= 42 u - 17 u
= 25 u

25 u = 175

1 u = 175 ÷ 25 = 7

Number of erasers that Henry gave to Hazel
= 6 u
= 6 x 7
= 42

Answer(s): 42